First I'd like to clear up some confusion on How the Element Repository Works. If a new element is added each time you click the button when the text differs, then it likely does not have a unique attribute (like ID or name) attached to it. My guess is that Test Studio is crafting the Find Expression of each newly added element based on text content. If that's the case you can easily edit the Find Expression to locate the element based on "textcontent contains logout".
To proceed in code you'll need to inspect the HTML surrounding that element. It seems Test Studio is referencing a <span> element and not a <button>. In that case you can use the following VB code:
HtmlSpan = Find.ByExpression(Of HtmlSpan)(
for whatever attribute you'd like, or only reference one attribute instead of two. See here
for more information.
You can also identify and act upon elements the standard way, but it's not as robust as the HTML Control Element Wrappers Suite:
Element = Find.ByExpression(
for more info.
the Telerik team